Related papers: A Spinor Approach to Penrose Inequality
Smooth deformations of a Minkowski type metric in a four-dimensional space-time manifold are considered. Deformations of the basic spin-tensorial fields associated with this metric are calculated and their application to calculating the…
New extrinsic lower bounds are given for the classical Dirac operator on the boundary of a compact domain of a spin manifold. The main tool is to solve some boundary problems for the Dirac operator of the domain under boundary conditions of…
We consider the energy spectrum and the spin-parity structure of the eigenstates for a quantum dot made of a strong topological insulator. Using the effective low-energy theory in a finite-length cylinder geometry, numerical calculations…
It is known that some results for spinors, and in particular for superenergy spinors, are much less transparent and require a lot more effort to establish, when considered from the tensor viewpoint. In this paper we demonstrate how the use…
We consider a spinorial Yamabe-type problem on open manifolds of bounded geometry. The aim is to study the existence of solutions to the associated Euler-Lagrange-equation. We show that under suitable assumptions such a solution exists. As…
In this paper we prove an initial data rigidity result \`a la Eichmair, Galloway and Mendes (arXiv:2009.09527) using Dirac operator techniques. It applies to initial data sets on spin bands that satisfy the dominant energy condition, a…
Based on the $\mu$-bubble method we are able to prove the following version of Riemannian Penrose inequality without horizon: if $g$ is a complete metric on $\mathbb R^3\setminus\{O\}$ with nonnegative scalar curvature, which is…
The aim of this paper is to extend some basic results about marginally outer trapped surfaces to the context of surfaces having general null expansion. Motivated in part by recent work of Chai-Wan, we introduce the notion of…
This paper studies the two-component spinor form of massive spin-3/2 potentials in conformally flat Einstein four-manifolds. Following earlier work in the literature, a non-vanishing cosmological constant makes it necessary to introduce a…
We prove energy estimates for solutions to a tensorial system of coupled non-linear wave equations, in a way that is suitable to deal with the structure of the non-linearity that arises from the Einstein-Yang-Mills system in the Lorenz…
Since its introduction in 1962, the Newman-Penrose formalism has been widely used in analytical and numerical studies of Einstein's equations, like for example for the Teukolsky master equation, or as a powerful wave extraction tool in…
We obtain the approximate relativistic bound state of a spin-1/2 particle in the field of the Yukawa potential and a Coulomb-like tensor interaction with arbitrary spin-orbit coupling number k under the spin and pseudospin (p-spin)…
We develop the differential theory of complex spinorial forms associated with irreducible complex spinors across all dimensions and signatures. This framework enables the study of constrained parallelicity conditions for irreducible complex…
We study the effects of the tensor force, present in modern effective nucleon-nucleon interactions, in the spin instability of nuclear and neutron matter. Stability conditions of the system against certain very low energy excitation modes…
This paper explores the conditions under which modified gravitational theories admit the positive mass. Following Witten's spinor argument, it is argued that a single condition should be imposed upon a gauge connection in the…
The genuine Kaluza-Klein-like theories--with no fields in addition to gravity--have difficulties with the existence of massless spinors after the compactification of some space dimensions \cite{witten}. We proposed in previous paper a…
We study the existence of solutions to the spinorial Yamabe equation -- that is, the Euler--Lagrange equation associated with the conformal invariant introduced by S. Raulot -- for compact manifolds with boundary. For the inhomogeneous…
For the weighted Dirac eigenproblem on a compact spin manifold with the chiral boundary condition \begin{equation*} \left\{ \begin{array}{ll} D\varphi = \lambda f\varphi & \text{in } M, \\ \mathbf{B}\varphi = 0 & \text{on } \partial M,…
We present a method giving a spinorial characterization of an immersion in a product of spaces of constant curvature. As a first application we obtain a proof using spinors of the fundamental theorem of immersion theory in that spaces. We…
In this paper, we prove the spacetime positive mass theorem for asymptotically flat spin initial data sets with arbitrary ends and a non-compact boundary. Moreover, we demonstrate a quantitative shielding theorem, subject to the tilted…